The Three Loop Isotopy and Framed Isotopy Invariants of Virtual Knots

This paper introduces two virtual knot theory ``analogues'' of a well-known family of invariants for knots in thickened surfaces: the Grishanov-Vassiliev finite-type invariants of order two. The first, called the three loop isotopy invariant, is an invariant of virtual knots while the second, called the three loop framed isotopy invariant, is a regular isotopy invariant of framed virtual knots. The properties of these invariants are investigated at length. In addition, we make precise the informal notion of ``analogue''. Using this formal definition, it is proved that a generalized three loop invariant is a virtual knot theory analogue of a generalization of the Grishanov-Vassiliev invariants of order two

Khovanov Homology, Lee Homology and a Rasmussen Invariant for Virtual Knots

The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordisms which directly applies to classical knot and classical knot cobordisms. To do so, we give an alternate formulation for the Manturov definition of Khovanov homology for virtual knots and links with arbitrary coefficients. This approach uses cut loci on the knot diagram to induce a conjugation operator in the Frobenius algebra. We then discuss the implications of the maps induced in the aforementioned theory to the universal Frobenius algebra for virtual knots. Next we show how one can apply the Karoubi envelope approach of Bar-Natan and Morrison on abstract link diagrams with cross cuts to construct the canonical generators of the Khovanov-Lee homology. Using these canonical generators we derive a generalization of the Rasmussen invariant for virtual knot cobordisms and furthermore generalize Rasmussen's result on the slice genus for positive knots to the case of positive virtual knots. It should also be noted that this generalization of the Rasmussen invariant provides an easy to compute obstruction to knot cobordisms in $S_g \times I \times I$ in the sense of Turaev

Promoting REU participation from students in underrepresented groups

Research experiences for undergraduates (REUs) are an important component of undergraduate education. However, at the 2012 Trends in Undergraduate Research in the Mathematical Sciences conference, questions were raised about why many REU programs see few applications from students that are members of underrepresented groups. We examine the benefits of REUs and factors preventing or promoting participation in REUs

Perpetrating Cyber Dating Abuse: A Brief Report on the Role of Aggression, Romantic Jealousy and Gender

There is increasing evidence that the use of elec-tronic communication technology (ECT) is being integrated into romantic relationships, which can be used as a medium to control a romantic partner. Most research focuses on the vic-tims of cyber dating abuse, however, we focused on the factors that predict perpetration of cyber dating abuse. We explored whether aggression (verbal aggression, physical aggression, anger and hostility), romantic jealousy (emotional, cognitive and behavioral jealousy), and gender predicted perpetration of cyber dating abuse (n = 189). We found that hostility, behav-ioral jealousy and gender significantly predicted perpetration of cyber dating abuse. The findings of this study contribute to our understanding of the psychological factors that drive cyber dating abuse in romantic relationships

Eccentric Exercise Facilitates Mesenchymal Stem Cell Appearance in Skeletal Muscle

Eccentric, or lengthening, contractions result in injury and subsequently stimulate the activation and proliferation of satellite stem cells which are important for skeletal muscle regeneration. The discovery of alternative myogenic progenitors in skeletal muscle raises the question as to whether stem cells other than satellite cells accumulate in muscle in response to exercise and contribute to post-exercise repair and/or growth. In this study, stem cell antigen-1 (Sca-1) positive, non-hematopoetic (CD45-) cells were evaluated in wild type (WT) and α7 integrin transgenic (α7Tg) mouse muscle, which is resistant to injury yet liable to strain, 24 hr following a single bout of eccentric exercise. Sca-1+CD45− stem cells were increased 2-fold in WT muscle post-exercise. The α7 integrin regulated the presence of Sca-1+ cells, with expansion occurring in α7Tg muscle and minimal cells present in muscle lacking the α7 integrin. Sca-1+CD45− cells isolated from α7Tg muscle following exercise were characterized as mesenchymal-like stem cells (mMSCs), predominantly pericytes. In vitro multiaxial strain upregulated mMSC stem cells markers in the presence of laminin, but not gelatin, identifying a potential mechanistic basis for the accumulation of these cells in muscle following exercise. Transplantation of DiI-labeled mMSCs into WT muscle increased Pax7+ cells and facilitated formation of eMHC+DiI− fibers. This study provides the first demonstration that mMSCs rapidly appear in skeletal muscle in an α7 integrin dependent manner post-exercise, revealing an early event that may be necessary for effective repair and/or growth following exercise. The results from this study also support a role for the α7 integrin and/or mMSCs in molecular- and cellular-based therapeutic strategies that can effectively combat disuse muscle atrophy

Global disparities in SARS-CoV-2 genomic surveillance

Genomic sequencing is essential to track the evolution and spread of SARS-CoV-2, optimize molecular tests, treatments, vaccines, and guide public health responses. To investigate the global SARS-CoV-2 genomic surveillance, we used sequences shared via GISAID to estimate the impact of sequencing intensity and turnaround times on variant detection in 189 countries. In the first two years of the pandemic, 78% of high-income countries sequenced >0.5% of their COVID-19 cases, while 42% of low- and middle-income countries reached that mark. Around 25% of the genomes from high income countries were submitted within 21 days, a pattern observed in 5% of the genomes from low- and middle-income countries. We found that sequencing around 0.5% of the cases, with a turnaround time <21 days, could provide a benchmark for SARS-CoV-2 genomic surveillance. Socioeconomic inequalities undermine the global pandemic preparedness, and efforts must be made to support low- and middle-income countries improve their local sequencing capacity

Global disparities in SARS-CoV-2 genomic surveillance

Genomic sequencing is essential to track the evolution and spread of SARS-CoV-2, optimize molecular tests, treatments, vaccines, and guide public health responses. To investigate the global SARS-CoV-2 genomic surveillance, we used sequences shared via GISAID to estimate the impact of sequencing intensity and turnaround times on variant detection in 189 countries. In the first two years of the pandemic, 78% of high-income countries sequenced >0.5% of their COVID-19 cases, while 42% of low- and middle-income countries reached that mark. Around 25% of the genomes from high income countries were submitted within 21 days, a pattern observed in 5% of the genomes from low- and middle-income countries. We found that sequencing around 0.5% of the cases, with a turnaround time <21 days, could provide a benchmark for SARS-CoV-2 genomic surveillance. Socioeconomic inequalities undermine the global pandemic preparedness, and efforts must be made to support low- and middle-income countries improve their local sequencing capacity